Powerpoint
A Powerpoint presentation version of this document can be downloaded here:
Computational Approaches to Structural Design of Buildings.ppt

References
PDFs of four out of the six papers researched in this report are avaliable in the references section.

Introduction

Optimization of a building structure is a complicated task.  The steel skeletal structures in tall buildings are very complicated systems that must never fail.  These structures can usually be broken down into a system of columns, beams, and wind bracings, all of which can be modeled as simple beam and truss structures.  With the increasing popularity and computing power of computers, the place for computers in design is greater than ever, especially in optimization.  But when is a design optimal?  Is an optimized design strictly the one that uses the least material and is sufficiently strong?  Civil Engineers often look at the beauty of a design by how well it parallels nature, which tends to create efficient and symmetrical designs.  On the other hand, if all designs were optimized toward one scheme, virtually all bridges and buildings would look the same.  Architects tend to focus more on the aesthetic design of a structure.  Asymmetry can be intriguing and striking, while innovative truss designs can add character as well as a sound structural basis for a building.  This report examines three computational methods of optimization of building structures, two of which allow for unique but still optimal designs to be generated. 

Most optimization schemes for building structures can be broken down into two parts, the mathematical relations that solve for the desired parameter to be optimized (ie. stress), and the numerical methods used to search the problem space for the optimum solution.  The methods discussed in this report fall into this latter category.  Nevertheless, a brief discussion of the mathematics behind this analysis will be discussed here.

Analysis of a computer model is governed by mathematical and physical laws.  These mathematical relations provide the foundation of virtually all computational structural optimization algorithms.  A common method for determining stresses, forces, and displacements, is to use a similar method to using Kirchoff’s node law and Ohm’s law to solve for electrical currents and voltages.  This method also models the beams and trusses of a structure as a network of one-dimensional elements with the primary difference being that the forces and displacements are vectors instead of the scalar quantities used when analyzing voltages and currents as seen in the figure below where (b) is the electrical analog of a structural problem (a).  Applying this concept further by shrinking these beams and trusses down to very large but finite arrays of small sized elements allows for analysis of complex geometries.  This method is better known as the finite element method, and is how almost all stresses and strains are determined computationally.  The stress analysis criteria of all of the structural optimization methods discussed in this report are also based on this finite element method. [6]

By using these mathematical relations and searching the design space of potential outcomes based on varying each parameter, optimal designs can be found.  The methodology of searching this design space is the focus of the rest of this report. 

Click here to continue to the Overview of Methods section.